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mgmatps4

by stubbornp » Sun Oct 19, 2008 11:54 pm
If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?


1.[10,000z + 100z(x – y) – xyz]/10,000


2.[10,000z + 100z(y – x) – xyz]/10,000


3.100z(x – y) – xyz/10,000


4.100z(y – x) – xyz/10,000


5.10,000/100yz + xy


Please explain...
Last edited by stubbornp on Mon Oct 20, 2008 11:50 am, edited 1 time in total.
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Re: mgmatps4

by Stuart@KaplanGMAT » Mon Oct 20, 2008 12:54 am
stubbornp wrote:If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?


1.10,000z + 100z(x – y) – xyz/10,000


2.10,000z + 100z(y – x) – xyz/10,000


3.100z(x – y) – xyz/10,000


4.100z(y – x) – xyz/10,000


5.10,000/100yz + xy


Please explain...
We can do this either algebraically or by picking numbers. However, since the correct choice appears to be missing, picking numbers won't really work! We could also do this via common sense, an oft overlooked strategy on the GMAT.

Algebra:

If we mark up by x%, then we multiply by (100+x)/100.

If we mark down by y%, then we multiply by (100-y)/100.

So, our final price is:

(z)(100+x)(100-y)/(100)(100)
(100z + zx)(100-y)/10000
(10000z - 100zy + 100zx - zxy)/10000
10000z/10000 + 100(zx - zy)/10000 - zxy/10000
z + z(x-y)/100 - zxy/10000

which doesn't match any of your choices, which leads me to believe that you posted the answers incorrectly (because me making a mistake is unpossible! 8) ).

Common Sense

Anything with 10000z in it is WAY too big a number.

100z(x-y) or 100z(y-x) is either going to be super big positive or super big negative, also making no sense.

10000/100yx is equal to 100/yx. It's a safe bet that on test day, you won't see a non-reduced fraction as the correct answer.

So, using common sense we can elminate a, b, c, d AND e. Accordingly, choose:

(f) the correct answer is missing.

:lol:
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correct answer

by varunjyoti » Mon Oct 20, 2008 2:31 am
correct answer is 1.
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Re: mgmatps4

by stop@800 » Mon Oct 20, 2008 3:27 am
Stuart Kovinsky wrote:
stubbornp wrote:If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?


1.10,000z + 100z(x – y) – xyz/10,000


2.10,000z + 100z(y – x) – xyz/10,000


3.100z(x – y) – xyz/10,000


4.100z(y – x) – xyz/10,000


5.10,000/100yz + xy


Please explain...
We can do this either algebraically or by picking numbers. However, since the correct choice appears to be missing, picking numbers won't really work! We could also do this via common sense, an oft overlooked strategy on the GMAT.

Algebra:

If we mark up by x%, then we multiply by (100+x)/100.

If we mark down by y%, then we multiply by (100-y)/100.

So, our final price is:

(z)(100+x)(100-y)/(100)(100)
(100z + zx)(100-y)/10000
(10000z - 100zy + 100zx - zxy)/10000
10000z/10000 + 100(zx - zy)/10000 - zxy/10000
z + z(x-y)/100 - zxy/10000

which doesn't match any of your choices, which leads me to believe that you posted the answers incorrectly (because me making a mistake is unpossible! 8) ).

Common Sense

Anything with 10000z in it is WAY too big a number.

100z(x-y) or 100z(y-x) is either going to be super big positive or super big negative, also making no sense.

10000/100yx is equal to 100/yx. It's a safe bet that on test day, you won't see a non-reduced fraction as the correct answer.

So, using common sense we can elminate a, b, c, d AND e. Accordingly, choose:

(f) the correct answer is missing.

:lol:
A becomes the answer if I change
10,000z + 100z(x – y) – xyz/10,000
to

[10,000z + 100z(x – y) – xyz ] / 10000

so I think stubbornp has missed the braces :)
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by stubbornp » Mon Oct 20, 2008 11:49 am
All,

I apologies for missing those braces...

@stop@800,Thanks for correction...
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